Power inverter help, BEEPS constant when left in ON position,so I have to turn off/on

Hey guys, I'm new hear and I've got a question for you about my power inverter.
I have a Jensen 160watt cont and 300watt peak. I want to put my xbox in the car with this inverter and the real problem is when everything is plugged in meaning the power inverter is plugged in the cigarette lighter plug (i have 3 cig plugs and the one for the inverter is for sure rated 120watts max and meant for heavier use) and the xbox is plugged into the inverter. Now when I turn the power switch located on the inverter to the on position it glows red meaning its ready and i power the xbox up and it works. So here's the crappy part. When I shut off the car and come back to turn on the engine the power inverter emits a constant buzz which actually means i have to turn the switch on the power inverter off then back to on thus enabling it to function normally again. Now that is stoopid.
How do I get around that? Do I make an extended switch of that on/off switch and place it close to the driver area so that I can manually press it EVERYTIME? I wouldnt want to though. Is there a way to build a switch or somethign that will trick the inverter into booting safely when i stick the key in?

Thanks for replying to my thread. What I mainly wanted to do is just put something there that would somehow reset the inverter while the unit is always in the on position to by pass manually switching off then on and skipping the beep at the same time. Or anything that would make it automatic and not have me reach for it in the trunk all the time. BTW, It makes a long beeeeeeeeep which means i have to turn it off and back on to use properly.

if you're comfortable with your wiring knowlege, (i should have been into details, sorry) you can take the inverter appart and wire a relay to the on/off switch. Then connect the relay to a power source that comes on/off when you turn the key. That will it will mimic you flicking the switch on and off when you turn the ignition/acc on and off. After doing that, hard wire your inverter into a constant (always on) 12v+ source that has a big enough wire (ex: not a tiny light wire)

You could just try to make a better power connection for the inverter instead of the 12v acc plug. I used to get a buzzer noise from my inverter untill I used some 10ga wire and grounded it to the chassis and the power wire to my 2ga amp wire terminal block.

On another note, what kinda audio connection are you using to get audio from your xbox to your stereo? RF modulator, or do you have an RCA style input on your radio?